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C
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Difficulty:
15%
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Question Stats:
77% (01:13) correct
23%
(01:27)
wrong
based on 398
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If n is a positive integer, the sum of the integers from 1 to n, inclusive, equals \(\frac{(n(n+1))}{2}\) Which of the following equals the sum of the integers from 1 to 2n, inclusive?
A. \(n(n+1)\)
B. \(\frac{(n(2n+1))}{2}\)
C. \(n(2n+1)\)
D. \(2n(n+1)\)
E. \(2n(2n+1)\)
A. \(n(n+1)\)
B. \(\frac{(n(2n+1))}{2}\)
C. \(n(2n+1)\)
D. \(2n(n+1)\)
E. \(2n(2n+1)\)
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30 Oct 2018, 01:29
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pushpitkc
sum of the integers from 1 to n, inclusive, equals \(\frac{(n(n+1))}{2}\)
Replacing \(n\) by \(2n\)
sum of the integers from 1 to \(2n\), inclusive, equals \(\frac{(2n(2n+1))}{2} = n(2n+1)\)
Answer: Option C
28 Dec 2020, 10:17
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pushpitkc
An alternative approach is to test a certain value of n.
Let's say n = 3
So, 2n = 6, which means we want to find the sum of the integers from 1 to 6 inclusive
1 + 2 + 3 + 4 + 5 + 6 = 21
In other words, when n = 3, the answer to the question is 21
At this point, we'll take each answer choice, and replace n with 3 to see which one yields and outcome of 21
A. \(n(n+1)=3(3+1)=12\) No good. We want the outcome to be 21
B. \(\frac{(n(2n+1))}{2}=\frac{3(2(3)+1)}{2=10.5}\) No good. We want the outcome to be 21
C. \(n(2n+1)=3(2(3)+1)=21\) PERFECT!!!
D. \(2n(n+1)=2(3)(3+1)=24\) No good. We want the outcome to be 21
E. \(2n(2n+1)=2(3)(2(3)+1)=42\) No good. We want the outcome to be 21
Answer: C
